Question

How do free energy and entropy relate?

Answer 1

Hint :Entropy is the amount of thermal energy in a system per unit temperature that can't be used to do useful work. Gibbs free energy, also known as Gibbs energy, or free energy, is a quantity used to quantify the overall amount of work performed in a system when temperature and pressure remain constant.

Complete Step By Step Answer:
The Gibbs free energy of a system is defined as its enthalpy minus the product of its temperature and entropy at any given time.
 $G=H-TS$
where $G$ represents Gibbs free energy,
 $H$ represents Enthalpy,
 $T$ represents temperature, and
 $S$ represents Entropy.
During a reaction, the change in the Gibbs free energy of the system is equal to the change in the system's enthalpy minus the change in the product of the temperature and the entropy of the system.
 $G=\mathrm{\Delta }H-\mathrm{\Delta }(TS)$
If we assume the reaction to take place at a fixed temperature, then the equation becomes,
 $\mathrm{\Delta }G=\mathrm{\Delta }H-T\mathrm{\Delta }S$
Under any set of conditions, the change in a system's free energy that occurs during a reaction can be determined. The standard-state free energy of reaction is calculated using data obtained under standard-state $(\mathrm{\Delta }{G}^{\circ })$
 $\mathrm{\Delta }{G}^{\circ }=\mathrm{\Delta }{H}^{\circ }-T\mathrm{\Delta }{S}^{\circ }$
When measuring $\mathrm{\Delta }{G}^{\circ }$ for a reaction, the entropy term is subtracted from the enthalpy term.

Note :
 $\mathrm{\Delta }{G}^{\circ }$ is negative for any reaction in which $\mathrm{\Delta }{H}^{\circ }$ is negative and $\mathrm{\Delta }{S}^{\circ }$ is positive due to the way the system's free energy is calculated. For any reaction that is preferred by both the enthalpy and entropy terms, $\mathrm{\Delta }{G}^{\circ }$ is negative. As a result, we can infer that any reaction with a negative $\mathrm{\Delta }{G}^{\circ }$ should be favourable or random.